A Data Mining Approach for Detecting Collusion in Unproctored Online Exams

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# A Data Mining Approach for Detecting Collusion in Unproctored Online Exams<br>

.padding_left.pull-down.white[
J. Langerbein, T. Massing, .bold[_J. Klenke_],  M. Striewe, M. Goedicke, C. Hanck, N. Reckmann
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`$15^{th}$` International Conference on Educational Data Mining

Bangalore, 11-24 July, 2023
]

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<h1> Outline </h1>

`$\quad$`
1. [Introduction](#introduction)
1. [Related work](#related_work)
1. [Methodology](#methodology)
1. [Empirical Results](#empirical_results)
1. [Discussion](#discussion)
1. [References](#references)

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name: introduction

<h1> Introduction </h1>

* COVID-19 forced universities to switch to online classes and exams.
* Proctoring online exams with video conference software was often prohibited due to data protection regulations and economically unfeasible.
* In this case study take-home exams were conducted as open-book, but collaboration was strictly prohibited.
* Hierarchical clustering algorithms were used to identify groups of potentially colluding students.
* The method successfully found groups with nearly identical exams.
* A proctored comparison group helped categorize student groups as "outstandingly similar".

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name: related_work

<h1> Related work </h1>

* Limited research exists on unproctored exams at universities prior to the pandemic.
* <a href='#bib-cleophas2021s'>Cleophas et al. (2021)</a> propose a method using event logs to detect collusion in unproctored exams.
* Previous studies focused on similarity measures for programming exams based on keyboard patterns, e.g. <a href='#bib-Hellas_2017'>Hellas et al. (2017)</a> and <a href='#bib-Leinonen_2016'>Leinonen et al. (2016)</a>.
* Other literature (e.g. <a href='#bib-hemming2010online'>Hemming (2010)</a>) relies on surveys or interviews, lacking actual student behavior data on collusion.
* Some studies suggest that unsupervised online exams may lead to collusion.
* <a href='#bib-hollister2009proctored'>Hollister and Berenson (2009)</a> used GPA and final exam scores to analyze collusion but not data collected during the exam.

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name: methodology

<h1> Methodology — <span style="font-size: 0.8em;"> Model </span> </h1>

* Data for the study was collected from the *Descriptive Statistics* course at the University Duisburg-Essen, Germany.
* The test group took the unproctored exam at home during the COVID-19 pandemic, while the comparison group took a proctored exam in class before the pandemic.
* The exams consisted of arithmetical problems, programming tasks in `R`, and a short essay task.
* Event logs captured students' activities and time stamps during the exams, and points achieved per task were recorded.
* Data cleaning was conducted, removing students with minimal participation or achievement, as well as those with reported internet problems.
* Despite differences in exam format, both groups shared similar content and learning goals, with opportunities for questions and discussions.
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<h1> Methodology — <span style="font-size: 0.8em;"> Data set </span> </h1>

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<table style="width:100%">
  <tr>
    <th> </th>
    <th>Comparison group</th>
    <th>Test group</th>
  </tr>
  <tr>
    <th>Year</th>
    <td>2018/2019</td>
    <td>2020/2021</td>
  </tr>
  <tr>
    <th>N</th>
    <td>109</td>
    <td>151</td>
  </tr>
    <tr>
    <th>Style</th>
    <td>proctored (in class)</td>
    <td>unproctored (at home)</td>
  </tr>
    <tr>
    <th>Total points</th>
    <td>60</td>
    <td>60</td>
  </tr>
    <tr>
    <th>Sub tasks</th>
    <td>19</td>
    <td>17</td>
  </tr>
    <tr>
    <th>Minutes</th>
    <td>60</td>
    <td>60</td>
  </tr>
</table>

</body>
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---

<h1> Methodology — <span style="font-size: 0.8em;"> Model </span> </h1>

* Agglomerative (bottom-up) hierarchical clustering algorithm
* Global pairwise dissimilarities

`$$D(x_i, x_{i'}) = \frac{1}{h} \sum_{j=1}^h w_j \cdot d_j(x_{ij}, x_{i'j}) \quad with \quad \sum_{j=1}^h w_j = 1$$`
* `$D(x_i, x_{i'})$`: Global pairwise dissimilarity
* `$d_j(x_{ij}, x_{i'j})$`: Pairwise attribute dissimilarity
* `$i = 1, ..., N$` with `$N = 151$` students
* `$j = 1, ..., h$` attributes
* We compared two different kinds of attributes:
  * Dissimilarities in the student´s event patters (time of submission)
  * Dissimilarities in points achieved
  
---

<h1> Methodology — <span style="font-size: 0.8em;"> Model </span> </h1>

### Dissimilarities in the student´s event patters (time of submission)

* `$d_j^L(v_{ij}, v_{i'j})$` with weights `$w_j^L$`
* We divided the examination into `$m = 1, ... , 70$` intervals, since both exams took `$70$` min.
* `$v_{ijm}$` denotes the count of answers of student `$i$` during the `$m$`-th interval.
* Manhatten metric used for calculation of the pairwise attribute dissimilarity.

`$\quad$`
  
`$$d_j^L(v_{ij}, v_{i'j}) = \sum_{m=1}^{K=70} | v_{ijm} - v_{i'jm} |$$`
  
---
  
<h1> Methodology — <span style="font-size: 0.8em;"> Model </span> </h1>
  
### Dissimilarities in points achieved

* `$d_j^P(s_{ij}, s_{i'j})$` with weights `$w_j^P$`
* `$s_{ij}$` denotes the points achieved by student `$i$` in the `$j$`-th sub task.
* Absolute difference used as dissimilarity measure.

`$\quad$`
  
`$$d_j^P(s_{ij}, s_{i'j}) = |  s_{ij} - s_{i'j} |$$`

---

<h1> Methodology — <span style="font-size: 0.8em;"> Model </span> </h1>

### Full model

`$$D(s_i, s_{i'}, v_i, v_{i'}) = \frac{1}{h} \sum_{j=1}^h (w_j^P \cdot d_j^P (s_{ij}, s_{i'j}) + w_j^L \cdot d_j^L (v_{ij}, v_{i'j}))
\quad \text{with} \quad \sum_{j=1}^h w_j^P + w_j^L =1$$`

* Weights `$w_j$` control the influence each attribute on the global object dissimilarity.
* We reduced the weights for: 
  * `R`-tasks and free-text questions, since the event log might not be comparable in these cases
  * Points achieved
* Since dissimilarity measures depend on scale, the attributes were normalized.

---

<h2>Empirical results — <span style="font-size: 0.8em;">Dendogram</span></h2>

.panelset.sideways[
.panel[.panel-name[Control group]

<div class="figure" style="text-align: center">
<img src="data:image/png;base64,#../resources/graphics/dendogram_control.png" alt="&lt;strong&gt; Figure 1: &lt;/strong&gt; Dendogram produced by average linkage clustering of the proctored control group (2018/19). &lt;strong&gt; G-L &lt;/strong&gt; mark the clusters with the lowest dissimilarity" width="150%" />
<p class="caption"><strong> Figure 1: </strong> Dendogram produced by average linkage clustering of the proctored control group (2018/19). <strong> G-L </strong> mark the clusters with the lowest dissimilarity</p>
</div>
]

.panel[.panel-name[Test group]

<div class="figure" style="text-align: center">
<img src="data:image/png;base64,#../resources/graphics/dendogram_test.png" alt="&lt;strong&gt;Figure 2:&lt;/strong&gt;  Dendogram produced by average linkage clustering of the unproctored test group (2020/21). &lt;strong&gt; A-F &lt;/strong&gt; mark the clusters with the lowest dissimilarity." width="100%" />
<p class="caption"><strong>Figure 2:</strong>  Dendogram produced by average linkage clustering of the unproctored test group (2020/21). <strong> A-F </strong> mark the clusters with the lowest dissimilarity.</p>
</div>
]
]

<h3 style="margin-bottom: -15px;">Results</h3>
<p style="margin-top: 0; font-size: 70%;">
<ul>
    <li>The control group has an overall higher level of dissimilarity and doesn´t contain any strikingly similar cluster.
    The six lowest cluster from the test group stand out in terms of similarity, specially cluster <strong>A</strong>, <strong>B</strong> and <strong>E</strong>.</li>
</ul>
</p>

---

<h2>Empirical results — <span style="font-size: 0.8em;">Distribution of measured distances </span> </h2>

.pull-left[
<div class="figure" style="text-align: center">
<img src="data:image/png;base64,#../resources/graphics/boxplot_original.png" alt="&lt;strong&gt;Figure 3.1:&lt;/strong&gt; Comparison of the non-normalised distance measures." width="100%" height="60%" />
<p class="caption"><strong>Figure 3.1:</strong> Comparison of the non-normalised distance measures.</p>
</div>

]

.pull-right[
<div class="figure" style="text-align: center">
<img src="data:image/png;base64,#../resources/graphics/boxplot_comparison.png" alt="&lt;strong&gt;Figure 3.2:&lt;/strong&gt; Comparison of the  normalised distance measures." width="100%" height="60%" />
<p class="caption"><strong>Figure 3.2:</strong> Comparison of the  normalised distance measures.</p>
</div>
]

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<h2>Empirical results — <span style="font-size: 0.8em;">Cluster comparison</span></h2>

.panelset[
.panel[.panel-name[AB]

<div class="figure" style="text-align: center">
<img src="data:image/png;base64,#../resources/graphics/plot_ab.png" alt="&lt;strong&gt;Figure 4.1:&lt;/strong&gt; Comparison of the event logs and achieved points of the clusters &lt;strong&gt;A&lt;/strong&gt; and &lt;strong&gt;B&lt;/strong&gt; from the test group (2020/21). Above the scatter plot, a bar chart is added to compare the points per subtask." width="80%" />
<p class="caption"><strong>Figure 4.1:</strong> Comparison of the event logs and achieved points of the clusters <strong>A</strong> and <strong>B</strong> from the test group (2020/21). Above the scatter plot, a bar chart is added to compare the points per subtask.</p>
</div>
]

.panel[.panel-name[CD]

<div class="figure" style="text-align: center">
<img src="data:image/png;base64,#../resources/graphics/plot_cd.png" alt="&lt;strong&gt;Figure 4.2:&lt;/strong&gt; Comparison of the event logs and achieved points of the clusters &lt;strong&gt;C&lt;/strong&gt; and &lt;strong&gt;D&lt;/strong&gt; from the test group (2020/21). Above the scatter plot, a bar chart is added to compare the points per subtask." width="80%" />
<p class="caption"><strong>Figure 4.2:</strong> Comparison of the event logs and achieved points of the clusters <strong>C</strong> and <strong>D</strong> from the test group (2020/21). Above the scatter plot, a bar chart is added to compare the points per subtask.</p>
</div>
]

.panel[.panel-name[EF]

<div class="figure" style="text-align: center">
<img src="data:image/png;base64,#../resources/graphics/plot_ef.png" alt="&lt;strong&gt;Figure 4.3:&lt;/strong&gt; Comparison of the event logs and achieved points of the clusters &lt;strong&gt;E&lt;/strong&gt; and &lt;strong&gt;F&lt;/strong&gt; from the test group (2020/21). Above the scatter plot, a bar chart is added to compare the points per subtask." width="80%" />
<p class="caption"><strong>Figure 4.3:</strong> Comparison of the event logs and achieved points of the clusters <strong>E</strong> and <strong>F</strong> from the test group (2020/21). Above the scatter plot, a bar chart is added to compare the points per subtask.</p>
</div>
]

.panel[.panel-name[GH]

<div class="figure" style="text-align: center">
<img src="data:image/png;base64,#../resources/graphics/plot_gh.png" alt="&lt;strong&gt;Figure 4.4:&lt;/strong&gt; Comparison of the event logs and achieved points of the clusters &lt;strong&gt;G&lt;/strong&gt; and &lt;strong&gt;H&lt;/strong&gt; from the control group (2018/19). Above the scatter plot, a bar chart is added to compare the points per subtask." width="80%" />
<p class="caption"><strong>Figure 4.4:</strong> Comparison of the event logs and achieved points of the clusters <strong>G</strong> and <strong>H</strong> from the control group (2018/19). Above the scatter plot, a bar chart is added to compare the points per subtask.</p>
</div>
]

.panel[.panel-name[IJ]

<div class="figure" style="text-align: center">
<img src="data:image/png;base64,#../resources/graphics/plot_ij.png" alt="&lt;strong&gt;Figure 4.5:&lt;/strong&gt; Comparison of the event logs and achieved points of the clusters &lt;strong&gt;I&lt;/strong&gt; and &lt;strong&gt;J&lt;/strong&gt; from the control group (2018/19). Above the scatter plot, a bar chart is added to compare the points per subtask." width="80%" />
<p class="caption"><strong>Figure 4.5:</strong> Comparison of the event logs and achieved points of the clusters <strong>I</strong> and <strong>J</strong> from the control group (2018/19). Above the scatter plot, a bar chart is added to compare the points per subtask.</p>
</div>
]

.panel[.panel-name[KL]

<div class="figure" style="text-align: center">
<img src="data:image/png;base64,#../resources/graphics/plot_kl.png" alt="&lt;strong&gt;Figure 4.6:&lt;/strong&gt; Comparison of the event logs and achieved points of the clusters &lt;strong&gt;K&lt;/strong&gt; and &lt;strong&gt;L&lt;/strong&gt; from the control group (2018/19). Above the scatter plot, a bar chart is added to compare the points per subtask." width="80%" />
<p class="caption"><strong>Figure 4.6:</strong> Comparison of the event logs and achieved points of the clusters <strong>K</strong> and <strong>L</strong> from the control group (2018/19). Above the scatter plot, a bar chart is added to compare the points per subtask.</p>
</div>
]

]

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<h1> Discussion </h1>

* The results of hierarchical clustering algorithms are presented in a dendrogram, providing a visual representation of the clustering results.
* A dendrogram resembles a tree structure, where objects are merged based on their dissimilarity in a bottom-up approach.
* Various hierarchical clustering algorithms exist, and the cophenetic correlation coefficient is used to assess how well each algorithm represents the original structure in the data.
* Average linkage clustering is deemed the most suitable algorithm for the analysis.
* The dendrogram shows compact clusters at medium dissimilarities, with three notable clusters (**A**, **B**, and **E**) consisting of two students each, indicating the absence of collusion in larger groups.
* Scatterplots and barcharts are used to examine the similarity of students' chronology and achieved points within clusters.

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name: discussion
<h1> Discussion </h1>

* Comparison with the results from the comparison group supports the findings, indicating that collusion over the entire exam is unlikely, and the differences between the groups are not coincidental.
* The method successfully detects at least three clusters with near identical exams.
* The approach provides a basis for further examination of clusters based on comparison with a reference group, but the ground truth is not known, limiting the certainty of conclusions.
* Nevertheless, the elevated risk of detection may indeed discourage students from cheating in unproctored exams. 
* This is not only a important step in adapting to the progressing digitization of education, but it also equips us better for unforeseen situations in the future, much like the COVID-19 pandemic.

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<h1> Further research </h1>

* Exploring the long-term effectiveness of the detection method in deterring students from colluding in exams, and its impact on academic integrity and student behavior.
* Development and implementation of methods to collect and analyze complementary evidence, with the aim of improving detection rates and understanding the extent of collusion among students.

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name: references
# References

.font80[

Cleophas, C., C. Hoennige, F. Meisel, and P. Meyer (2021). "Who's
Cheating? Mining Patterns of Collusion from Text and Events in Online
Exams". In: _Mining Patterns of Collusion from Text and Events in
Online Exams (April 12, 2021)_.

Hellas, A., J. Leinonen, and P. Ihantola (2017). _Plagiarism in
Take-Home Exams: Help-Seeking, Collaboration, and Systematic Cheating_.
ITiCSE '17. Bologna, Italy: Association for Computing Machinery, p.
238–243. ISBN: 9781450347044. DOI: 10.1145/3059009.3059065.
<https://doi.org/10.1145/3059009.3059065>.

Hemming, A. (2010). "Online tests and exams: lower standards or
improved learning?" In: _The Law Teacher_ 44.3, pp. 283-308.

Hollister, K. K. and M. L. Berenson (2009). "Proctored versus
unproctored online exams: Studying the impact of exam environment on
student performance". In: _Decision Sciences Journal of Innovative
Education_ 7.1, pp. 271-294.

Leinonen, J., K. Longi, A. Klami, A. Ahadi, and A. Vihavainen (2016).
_Typing patterns and authentication in practical programming exams_ ,
pp. 160-165.
]